SOLUTION: Rationalize the denominator of 7√3-5√2 divided by √48+√18
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Question 617255: Rationalize the denominator of 7√3-5√2 divided by √48+√18
Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!
Before going about rationalizing the denominator, I'm going to simplify the denominator. It will make the numbers smaller and easier to work with.
Now we'll rationalize. Rationalizing two-term denominators with square roots takes advantage of the pattern. The right side, as you can see is a difference of perfect squares. The left side is a product of two-term expressions. The pattern shows us how to take a two-term expression, an (a+b) or (a-b), and turn it into an expression of perfect squares.
Your denominator is a two-term sum. IOW, an (a+b). To turn it into an expression of perfect squares we need to multiply it by its corresponding (a-b):
Multiplying the denominators is easy; just use the pattern. To multiply the numerators we will need to use FOIL:
which simplifies as follows:
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